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What Does It Mean to Be Successful in Mathematics?
Pages 8-23

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Select key terms on the right to highlight them within pages of the chapter.


From page 9...
... Comprehending mathematical concepts, operations, and relations knowing what mathematical symbols, diagrams, and procedures mean. Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently, and appropriately.
From page 10...
... All young Americans must learn tothink mathematically if the United States istofosterthe educated workforce and citizenry tomorrow's world will demand. Understanding refers to a student's grasp of fundamental mathematical ideas.
From page 11...
... Computing includes being fluent with procedures for adding, subtracting, multiplying, and dividing mentally or with paper and pencil, and knowing when and how to use these procedures appropriately. Although the word computing implies an arithmetic procedure, in this document it also refers to being fluent with procedures from other branches of mathematics, such as measurement (measuring lengths)
From page 13...
... Understanding makes it easier to learn skills, while learning procedures can strengthen and develop mathematical understanding. Applying involves using one's conceptual and procedural knowledge to solve problems.
From page 14...
... Our view of mathematical proficiency goes beyond being able to understand, compute, apply, and
From page 16...
... Students who are proficient in mathematics believe that they can solve problems, develop understanding, and learn procedures through hard work, and that becoming mathematically proficient is worthwhile for them. Just as a stool cannot stand on one leg or even two, so mathematical proficiency cannot stand on one or two isolated strands.
From page 17...
... Addressing all the strands of proficiency makes knowledge stronger, more durable, more adaptable, more useful, and more relevant. Integrating the strands of mathematical proficiency is entirely consistent with students' typical approaches to learning.
From page 18...
... Research has shown, however, that students actually move through a fairly well-defined sequence of solution methods when they are learning to perform operations with single-digit numbers. This deeper understanding of student learning demonstrates how the four other strands of proficiency in addition to computing can be strengthened through the learning of number combinations.6 Understanding Number combinations are related.
From page 19...
... eighth graders. However, when students are encouraged to explore proportional situations in a variety of problem contexts, they naturally draw on all the strands of mathematical proficiency.
From page 20...
... They all understood that the relationship between the balloons and the dollars must remain the same, as Belinda's circles and column of $2s illustrate. Being fluent with various computational procedures such as counting, multiplying, and dividing helped each student attack the problem.
From page 21...
... When parents and teachers alike believe that hard work pays off, and when mathematics is taught and learned by using all the strands of proficiency, mathematics performance improves for all students. Careful research has demonstrated that mathematical proficiency is an obtainable goal.
From page 23...
... In the latter classrooms, teachers used mu Iti pie representations of mathematical ideas to support understanding, focused on nonroutine problems to strengthen application of concepts, emphasized mu Itiple sol utions to problems to develop computing fluency, and held classroom discus.


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